SQL Server 2019

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

CREATE TABLE HistoricCall
    ("projectId" varchar(6), "caseId" varchar(10), "callNumber" int, "callDate" datetime)
;

CREATE TABLE Responses
    ("projectId" varchar(6), "caseId" varchar(10), "cellmap" varchar(4))
;
    
INSERT INTO HistoricCall
    ("projectId", "caseId", "callNumber", "callDate")
VALUES
    ('637850', '0000000001', 1, '2014-09-11 16:32:11.000'),
    ('637850', '0000000001', 2, '2014-09-11 20:43:01.000'),
    ('637850', '0000000001', 3, '2014-09-12 21:09:55.000'),
    ('637850', '0000000001', 4, '2014-09-13 14:58:14.000'),
    ('637850', '0000000001', 5, '2014-09-14 16:42:27.000'),
    ('637850', '0000000001', 6, '2014-09-16 21:54:09.000'),
    ('637850', '0000000001', 7, '2014-09-16 22:30:24.000'), --Count 7
    ('637850', '0000000002', 1, '2014-09-11 16:36:17.000'),
    ('637850', '0000000002', 2, '2014-09-13 18:05:44.000'),
    ('637850', '0000000002', 3, '2014-09-14 20:39:55.000'), --Count 3
    ('100018', '0000000001', 1, '2014-09-15 17:05:03.000'),
    ('100018', '0000000001', 2, '2014-09-16 18:42:27.000'), -- Count 2
    ('100018', '0000000002', 1, '2014-09-17 14:55:19.000'),
    ('100018', '0000000002', 2, '2014-09-18 15:42:42.000'),
    ('100018', '0000000002', 3, '2014-09-19 17:02:24.000'), 
    ('100018', '0000000002', 4, '2014-09-20 16:17:02.000'), 
    ('100018', '0000000002', 5, '2014-09-21 13:10:15.000'), --Count 5 
    ('100018', '0000000003', 1, '2014-09-20 01:52:16.000'), 
    ('100018', '0000000003', 2, '2014-09-21 10:41:14.000') --Count 2 (skipped due to null cellmap)
    ;
    
INSERT INTO Responses
    ("projectId", "caseId", "cellmap")
VALUES
    ('637850', '0000000001', '9101'), --duplicate cellmap / different caseId (Count 3)
    ('637850', '0000000002', '9101'), --duplicate cellmap / different caseId (Count 7)
    ('637850', '0000000003', '5071'),
    ('637850', '0000000004', '5173'),
    ('637850', '0000000005', null),
    ('637850', '0000000006', '8062'),
    ('637850', '0000000007', '0012'),
    ('637850', '0000000008', '5292'),
    ('637850', '0000000009', '9230'),
    ('637850', '0000000010', '5187'),
    ('100018', '0000000001', '0118'),
    ('100018', '0000000002', '0999'),
    ('100018', '0000000003', null), --ignore null value
    ('100018', '0000000004', '0119'),
    ('100018', '0000000005', '7253')
    ;

34 rows affected

projectId	callDate	cellmap	Count
100018	2014-09-16	0118	2
100018	2014-09-21	0999	5
637850	2014-09-14	9101	3
637850	2014-09-16	9101	7